In reply to 54ms: It depends how you define winter alpine climbing. There are climbs that are easy access and not too serious. Cosmiques Arete, Petite Verte and those on the rock triangle of Mont Blanc du Tacul for example but these are comparatively short routes. The only one that I know you can get to without skis is the Petite Verte. It may be possible with the others but there is no guarantee. There is valley ice climbing in the Chamonix valley and loads more within 2 hours drive. For any of the more "classic" bigger alpine climbs I would strongly recommend getting in a couple of summer seasons beforehand and investing in some very good boots and clothing systems. Winter climbing in the alps leaves very little margin for error. When the weather turns it turns with a vengeance and the likely hood and scale of avalanches is increased dramatically.
Al